A Study of Fermi-LAT GeV gamma-ray Emission towards the Magnetar-harboring Supernova Remnant Kesteven 73 and Its Molecular Environment

We report our independent GeV gamma-ray study of the young shell-type supernova remnant (SNR) Kes 73 which harbors a central magnetar, and CO-line millimeter observations toward the SNR. Using 7.6 years of Fermi-LAT observation data, we detected an extended gamma-ray source ("source A") with the centroid on the west of the SNR, with a significance of 21.6 sigma in 0.1-300 GeV and an error circle of 5.4 arcminute in angular radius. The gamma-ray spectrum cannot be reproduced by a pure leptonic emission or a pure emission from the magnetar, and thus a hadronic emission component is needed. The CO-line observations reveal a molecular cloud (MC) at V_LSR~90 km/s, which demonstrates morphological correspondence with the western boundary of the SNR brightened in multiwavelength. The 12CO (J=2-1)/12CO (J=1-0) ratio in the left (blue) wing 85-88 km/s is prominently elevated to ~1.1 along the northwestern boundary, providing kinematic evidence of the SNR-MC interaction. This SNR-MC association yields a kinematic distance 9 kpc to Kes 73. The MC is shown to be capable of accounting for the hadronic gamma-ray emission component. The gamma-ray spectrum can be interpreted with a pure hadronic emission or a magnetar+hadronic hybrid emission. In the case of pure hadronic emission, the spectral index of the protons is 2.4, very similar to that of the radio-emitting electrons, essentially consistent with the diffusive shock acceleration theory. In the case of magnetar+hadronic hybrid emission, a magnetic field decay rate >= 10^36 erg/s is needed to power the magnetar's curvature radiation.Comment: 7 figures, published in Ap

Characterizing Deep Learning Package Supply Chains in PyPI: Domains, Clusters, and Disengagement

Deep learning (DL) package supply chains (SCs) are critical for DL frameworks to remain competitive. However, vital knowledge on the nature of DL package SCs is still lacking. In this paper, we explore the domains, clusters, and disengagement of packages in two representative PyPI DL package SCs to bridge this knowledge gap. We analyze the metadata of nearly six million PyPI package distributions and construct version-sensitive SCs for two popular DL frameworks: TensorFlow and PyTorch. We find that popular packages (measured by the number of monthly downloads) in the two SCs cover 34 domains belonging to eight categories. Applications, Infrastructure, and Sciences categories account for over 85% of popular packages in either SC and TensorFlow and PyTorch SC have developed specializations on Infrastructure and Applications packages respectively. We employ the Leiden community detection algorithm and detect 131 and 100 clusters in the two SCs. The clusters mainly exhibit four shapes: Arrow, Star, Tree, and Forest with increasing dependency complexity. Most clusters are Arrow or Star, but Tree and Forest clusters account for most packages (Tensorflow SC: 70%, PyTorch SC: 90%). We identify three groups of reasons why packages disengage from the SC (i.e., remove the DL framework and its dependents from their installation dependencies): dependency issues, functional improvements, and ease of installation. The most common disengagement reason in the two SCs are different. Our study provides rich implications on the maintenance and dependency management practices of PyPI DL SCs.Comment: Manuscript submitted to ACM Transactions on Software Engineering and Methodolog

A Model of Two-Way Selection System for Human Behavior

We propose a model of two-way selection system. It appears in the processes like choosing a mate between men and women, making contracts between job hunters and recruiters, and trading between buyers and sellers. In this paper, we propose a model of two-way selection system, and present its analytic solution for the expectation of successful matching total and the regular pattern that the matching rate trends toward an inverse proportion to either the ratio between the two sides or the ratio of the state total to the smaller people number. The proposed model is verified by empirical data of the matchmaking fairs. Results indicate that the model well predicts this typical real-world two- way selection behavior to the bounded error extent, thus it is helpful for understanding the dynamics mechanism of the real-world two-way selection system.Comment: 8 pages, 4 figure

Quantitative global well-posedness of Boltzmann-Bose-Einstein equation and incompressible Navier-Stokes-Fourier limit

In the diffusive scaling and in the whole space, we prove the global well-posedness of the scaled Boltzmann-Bose-Einstein (briefly, BBE) equation with high temperature in the low regularity space $H^2_xL^2$. In particular, we quantify the fluctuation around the Bose-Einstein equilibrium $\mathcal{M}_{\lambda,T}(v)$ with respect to the parameters $\lambda$ and temperature $T$. Furthermore, the estimate for the diffusively scaled BBE equation is uniform to the Knudsen number $\epsilon$. As a consequence, we rigorously justify the hydrodynamic limit to the incompressible Navier-Stokes-Fourier equations. This is the first rigorous fluid limit result for BBE.Comment: 42 page

On semi-classical limit of spatially homogeneous quantum Boltzmann equation: asymptotic expansion

We continue our previous work [Ling-Bing He, Xuguang Lu and Mario Pulvirenti, Comm. Math. Phys., 386(2021), no. 1, 143223.] on the limit of the spatially homogeneous quantum Boltzmann equation as the Planck constant $\epsilon$ tends to zero, also known as the semi-classical limit. For general interaction potential, we prove the following: (i). The spatially homogeneous quantum Boltzmann equations are locally well-posed in some weighted Sobolev spaces with quantitative estimates uniformly in $\epsilon$. (ii). The semi-classical limit can be further described by the following asymptotic expansion formula: $$f^\epsilon(t,v)=f_L(t,v)+O(\epsilon^{\vartheta}).$$ This holds locally in time in Sobolev spaces. Here $f^\epsilon$ and $f_L$ are solutions to the quantum Boltzmann equation and the Fokker-Planck-Landau equation with the same initial data.The convergent rate $0<\vartheta \leq 1$ depends on the integrability of the Fourier transform of the particle interaction potential. Our new ingredients lie in a detailed analysis of the Uehling-Uhlenbeck operator from both angular cutoff and non-cutoff perspectives.Comment: 32 pages

Quasi-Periodic Variations in X-ray Emission and Long-Term Radio Observations: Evidence for a Two-Component Jet in Sw J1644+57

The continued observations of Sw J1644+57 in X-ray and radio bands accumulated a rich data set to study the relativistic jet launched in this tidal disruption event. The X-ray light curve of Sw J1644+57 from 5-30 days presents two kinds of quasi-periodic variations: a 200 second quasi-periodic oscillation (QPO) and a 2.7-day quasi-periodic variation. The latter has been interpreted by a precessing jet launched near the Bardeen-Petterson radius of a warped disk. Here we suggest that the $\sim$ 200s QPO could be associated with a second, narrower jet sweeping the observer line-of-sight periodically, which is launched from a spinning black hole in the misaligned direction with respect to the black hole's angular momentum. In addition, we show that this two-component jet model can interpret the radio light curve of the event, especially the re-brightening feature starting $\sim 100$ days after the trigger. From the data we infer that inner jet may have a Lorentz factor of $\Gamma_{\rm j} \sim 5.5$ and a kinetic energy of $E_{\rm k,iso} \sim 3.0 \times 10^{52} {\rm erg}$, while the outer jet may have a Lorentz factor of $\Gamma_{\rm j} \sim 2.5$ and a kinetic energy of $E_{\rm k,iso} \sim 3.0 \times 10^{53} {\rm erg}$.Comment: 11 pages, 7 figures, accepted for publication in Ap